New trapdoor-knapsack public-key cryptosystem

Abstract

The paper presents a new trapdoor-knapsack public-key cryptosystem. The encryption equation is based on the general modular knapsack equation, but, unlike the Merkle-Hellman scheme, the knapsack components do not have to have a superincreasing structure. The trapdoor is based on transformations between the modular and radix form of the knapsack components, via the Chinese remainder theorem. The security is based on factoring a number composed of 256 bit prime factors. The resulting cryptosystem has high density, approximately 30% message expansion and a public key of 14 Kbits. This compares very favourably with the Merkle-Hellman scheme which has over 100% expansion and a public key of 80 Kbits. The major advantage of the scheme when compared with the RSA scheme is one of speed. Typically, knapsack schemes such as the one proposed here are capable of throughput speeds which are orders of magnitude faster than the RSA scheme.